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A new framework to design adaptive controllers for nonlinearly parameterized systems is proposed in this paper. The key step is the construction of a monotone function, which explicitly depends on some of the estimator tuning parameters. Monotonicity-or the related property of convexity-have already been explored by several authors with convexity being an a priori assumption that is valid only on some region of state space. In our approach monotonicity is enforced by the designer, effectively becoming a synthesis tool. One consequence of this fact is that the controller does not rely on state-dependent switching. In order to dispose of degrees of freedom to render the function monotone we depart from standard adaptive control and adopt instead the recently introduced Immersion and Invariance approach.